#### Market-Capitalization Weighted Portfolios: The Global Monkey by Winton Global Investment Management

*Randomly selected equally weighted portfolios have outperformed **market-capitalization weighted portfolios globally and **by region over the last fifteen years. These results and structural* *features of market-capitalization benchmarks call the supposed **efficiency of these benchmarks into question.*

In October 2011, David Harding published the results of our research into the efficiency, or otherwise, of market-capitalization weighted portfolios1. The core result was that randomly chosen equally weighted portfolios had outperformed the S&P 500 from 1965 through to 2011. Such a result clearly throws the efficiency of market-capitalization weighted portfolios into doubt. In more colloquial terms, a monkey throwing one hundred darts at a list of stocks in the index would likely have outperformed the supposedly efficient traditional benchmark. Furthermore, while it is possible that the portfolios randomly chosen outperform because they take on higher risk, which would not necessarily violate the Capital Asset Pricing Model (CAPM), they also have higher Sharpe ratios.

It is worthwhile to attempt a similar experiment on a global scale to see if the result is US-specific or on the contrary, if the monkey wins on a global basis (and if global CAPM is also violated). Using a similar approach to the original research, each year we randomly selected 20% of the average number of stocks for each of the regions in the MSCI global developed market index to obtain our portfolio constituents. We carried out this sampling 1000 times to obtain 1000 randomly generated portfolios. The performances of the random portfolios were then compared to market capitalization weighted regional indices that make up the MSCI World Index.

In Figure 1 we summarize the performance results for MSCI USA, MSCI Japan, MSCI Pacific excluding Japan, MSCI Europe and MSCI World. The darker blue line is the average performance of the randomly generated portfolios, the green line is the performance of the relevant index and the grey lines are the individual random portfolios.

The key result seems to hold globally. For all the regional portfolios and the MSCI World index itself, the randomly generated portfolios outperformed the index without taking on significantly more risk.

A widely used measure of portfolio efficiency is the Sharpe ratio, the ratio of expected return, minus the risk free-rate of interest, to the volatility of return. Accordingly, Table 1 shows the average Sharpe ratio and return for the random portfolios, and the Sharpe ratio and return for the corresponding index. If CAPM were true, it implies that investors should hold the market portfolio because it is the optimal portfolio of risky assets to hold. It is hard to reconcile this implication with the numbers in Table 1, which show that over the last 25 years, monkeygenerated portfolios have been superior in not only returns but also in terms of Sharpe ratios to the market-capitalization weighted portfolio in every region of the MSCI World index. It could be argued that these results are specific to these time periods; however, since 24 years is a long period, these results can hardly be regarded as a short-term anomaly.

There are other good reasons to doubt that market-capitalization weighted portfolios are the optimal risky asset portfolio as the global CAPM implies. Figure 2 shows the cumulative percentage of market capitalization accounted for by a given percentage of the number of stocks in the relevant regional index. The stocks are ordered by size and so, the largest stock is added first and the smallest stock is added last. The shape of the cumulative distribution is very similar in each region. A key result from this analysis is that a relatively small number of stocks account for a large proportion of the total market capitalization of each index. For example, in MSCI Europe the largest 20% of constituents account for roughly 60% of the overall market cap of the index. Similar results hold for the other regional indices. By contrast, if these indices were equally weighted then 20% of the index constituents would account for 20% of the market cap.

Another way of summarizing this data is in terms of concentration; the degree to which the overall distribution of weights is dominated by large weights on a few stocks. The Gini coefficient is a measure of concentration. For an equally weighted index the Gini coefficient is zero and ranges between 0 and 1 for other weight distributions where higher values indicate greater concentration. Table 2 shows the Gini coefficient for the various MSCI indices and the S&P500 index. As might be expected from the market capitalization distributions charts, these indices are very concentrated.

A good reason, therefore, to doubt the global CAPM is that this theory implies that every investor ought to hold stocks in precisely the highly concentrated weights of each regional index. To hold an equally weighted portfolio in this framework is to introduce a substantial “size exposure” relative to the market-capitalization weighted benchmark. If global CAPM does not hold then of course there may be no good reason to hold the market-capitalization weighted portfolio and it would seem more reasonable based on this analysis to regard it as having a substantial size exposure. In summary, of course the total holdings of equities must equal the total amount of equity outstanding but different investors may well prefer different portfolios and need not hold highly concentrated index portfolios.

A second issue with the global CAPM theory that follows trivially from the regional analysis is that all investors should hold the same capitalization-weighted global index as their equity allocation. This directly implies that the country weights in each investor’s portfolio should be equal to the country weights in the index, regardless of which country they live in. However, in practice, this is very far from being the case. Table 32 shows the percentage of market capitalization of each country in the index and the amount of that market held in domestic equity portfolios for selected countries. According to global CAPM these numbers should be the same3. Only a subset of major markets from the working paper is included; while Indonesia is not a big market, it is included as it has the largest home country bias in the world. So in every country, investors hold more of their domestic market in their portfolios than they should if global CAPM was right. A very large number of papers have attempted to reconcile this “Home equity bias” with global CAPM; however, so far this has been a fruitless task given the extent of the deviations from the theoretically implied portfolio proportions.

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